CN103068027A - Optimal power distribution method of multiple relays in frequency flat fading channel - Google Patents

Abstract

The invention discloses an optimal power distribution method of multiple relays in a frequency flat fading channel. For a two-bounce parallel direct amplification type (AF) relay network, under the condition of frequency flat fading, circuit processing power of a node is considered, and the optimal power distribution method under mixing power restraint is provided. Mixing power restraint means relay independent power restraint and relay and power restraint with upper limit restraint and lower limit restraint at the same time, and optimizing purpose is that output signal to noise ratio of a system is maximized. According to the method, performance comparison of system maximum output signal to noise ratio under several conditions is provided, simulation results show that when an upper limit restraint value of independent power restraint of a relay node is set, the bigger the lower limit restraint value is, the poorer the maximum signal to noise ratio performance output by the system is, when the upper limit restraint value and the lower limit restraint value of the independent power restraint of the relay node are set, the performance of a relay mixing optimal power distribution strategy is better than the performance of a relay equipower distribution strategy, and adding of system relay number can bring output signal to noise ratio gain for the system.

Description

The optimal power allocation method of many relayings under a kind of frequency flatness fading channel

Technical field

The present invention relates to the relay cooperative communication field, especially relate to the optimal power allocation method of many relayings under the frequency flatness fading channel.

Background technology

The research of relay cooperative communication problem starts from eighties of last century the seventies, Meulen[Meulen E C.Three-terminal communication channels[J] .Advances in Applied Probability, 1971,3:120-154] studied at first the trunk channel capacity of three nodes in 1971.Nowadays, along with the fast development of MIMO technique (MIMO), relay cooperative communication has become one of study hotspot of wireless communication field.

When reaching destination node according to sending information to of source node, the number of times that information is processed by via node can be divided into junction network: Two-Hop and multihop network.The comparatively typical application scenarios of Two-Hop has cellular system.What the present invention studied is the AF junction network problem of double bounce, and each relaying is settled single antenna.

Access channel (MAC) system about dual user, in the situation of each user as another one user's AF via node, [the Mesbah W such as Mesbash, Davidson T.Joint power and channel resource allocation for two-user orthogonal amplify-and-forward cooperation[J] .IEEE Transactions on Wireless Communications 2008,7 (11): 4681-4691.] provided the power distribution strategies that can obtain the optimum of large capacity region in 2008; [the Jafar S A such as Jafar, Gomadam K S, Huang C.Duality and rate optimization for multiple access and broadcast channels with amplify-and-forward relays[J] .IEEE Transactions on Information Theory, 2007,53 (10): 3350-3370] if proved the user to a plurality of AF relayings are arranged between the destination node in 2007, under relaying and power constraint, the MAC channel capacity zone that obtains during with the optimal power allocation strategy is identical with its corresponding antithesis broadcast channel capacity region, and this conclusion also is applicable to multihop network; AF junction network for the double bounce that contains a plurality of point-to-point systems, [the Phan K T such as Phan, Tho L N, Vorobyov S A, et al.Power allocation in wireless multi-user relay networks[J] .IEEE Transactions on Wireless Communications, 2009,8 (5): 2535-2545] in 2009 to maximizing minimum user's output signal-to-noise ratio, maximize whole point-to-point systems speed and, guarantee in the situation of signal to noise ratio greater than given thresholding of each user's output, making maximum user emission power minimize three kinds of situation power division problems is studied, three kinds of situations have same constraints, be that the user has and power constraint, relaying has the independent power constraint.

Generally speaking, the power optimization problem is the focus of studying in the relay cooperative communication, belongs to the category that resource is distributed.The prerequisite of above these methods is the processing of circuit power of having ignored node self, but considers the factor such as energy-conservation and volume, and some wireless cooperative network can't be ignored this point.This paper has added the processing of circuit power factor (PF) of via node in algorithm model, so that model tallies with the actual situation more.

Summary of the invention

Technical problem: the objective of the invention is for the parallel AF junction network of the double bounce in the frequency-flat channel decline situation, and in the situation of the processing of circuit power of consideration node self, a kind of optimal power allocation method of the many relayings based on the frequency flatness fading channel is provided, the Performance Ratio that the present invention has provided system's maximum output signal-to-noise ratio under several situations, simulation result shows, when the upper limit binding occurrence one of the independent power of relaying node constraint regularly, the maximum signal to noise ratio performance of the larger system of lower limit binding occurrence output is poorer; When the bound binding occurrence of the independent power of relaying node constraint is all given regularly, the performance of relaying mixing optimal power allocation strategy is better than the performance of relaying constant power allocation strategy; The increase meeting of system's relaying number brings the output signal-to-noise ratio gain for system.

Technical scheme: the object of the present invention's research is the junction network of double bounce, and network is made of a source node, a destination node and K AF relaying, has configured single antenna on each relaying.Suppose to exist than the strong shadow effect between source node and destination node, therefore the signal that source node sends can not directly arrive destination node.All are placed in relaying assistance source between source node and the destination node to the transfer of data of destination node.Further supposition relaying mode of operation is semiduplex, and the internodal collaboration mode of suppose relay is parallel schema, suppose that whole relayings are according to order given in advance, transmit data to destination node successively, then, packet assists to be transferred to destination node from source node through relaying needs K+1 time slot.The indexed set that represents whole relayings with mark R, namely

R={1,2,…,K}

Wherein K is positive integer, the number of expression relaying.

Data by source node in the transmission course of destination node, in the first time slot, source node transmits to whole via nodes, destination node is in closed condition.Represent the signal that source node sends with s, and suppose that the power of its transmission is P _s, then, the reception signal r of i via node _iFor

r _i=h _is+w _i

Wherein, i represents the ordinal number of via node, is positive integer; h _iBe the channel coefficients of source node to via node, w _iFor the relay reception noise component(s), suppose

The expression variance, w _iFor obeying The independent normal distribution that distributes.

In a follow-up K time slot, source node is in closed condition, and K via node is successively to the destination node the transmission of data.In K time slot, each time slot only has a via node to pass data to destination node, and remaining K-1 via node all is in closed condition.Behind K time slot, all via node is all finished once with destination node and is communicated by letter, and each relaying is only communicated by letter once.During the work of i relaying, it is r to the received signal first _iPower is amplified, and the signal after will amplifying again is toward the destination node transmission.Then, the transmitted signal t of i relaying _iFor

t _i＝α _ir _i

Wherein, α _iBe i the amplification factor that relaying is corresponding.So, the signal y from i via node that destination node receives _iFor

y _i=g _it _i+v _i=(α _ig _ih _i)s+(α _ig _iw _i+v _i)

Wherein, g _iRepresent i via node to the channel coefficients of destination node, v _iRepresent the reception noise component(s) on the destination node.

Behind the K+1 time slot, destination node obtains receiving vectorial y=[y ₁, y ₂, y _K] ^TSo source node can be regarded a single input multiple output system (SIMO) as to destination node, and get final product

y=hs+n (1)

Wherein

h=[α ₁g ₁h ₁,…,α _Kg _Kh _K] ^T，n=[α ₁g ₁w ₁+v ₁,…,α _Kg _Kw _K+v _K] ^T

H is channel, and n is noise vector.Suppose

Suppose that again whole noise component(s)s is statistics independently, therefore, the covariance matrix Λ of n is in the formula (1):

$\mathrm{\Λ}=E\left[{\mathrm{nn}}^{+}\right]=\mathrm{diag}[{\left|{\mathrm{\α}}_1{g}_1\right|}^2{{\mathrm{\σ}}_1}^2+{\mathrm{\σ}}_D^2,...,{\left|{\mathrm{\α}}_K{g}_K\right|}^2{\mathrm{\σ}}_K^2+{\mathrm{\σ}}_D^2]$

Wherein, diag represents diagonal matrix.[] ⁺Represent conjugate transpose.Suppose that again destination node knows the overall CSI of system, so destination node can be carried out to the vector that receives high specific and be merged, the maximum S/N R of gained is after merging

$\mathrm{SNR}={\left|\right|{\mathrm{\Λ}}^{-\frac{1}{2}}h\left|\right|}^2{P}_s=\underset{i\∈R}{\mathrm{\Σ}}\frac{{\left|{\mathrm{\α}}_i{g}_i{h}_i\right|}^2{P}_s}{{\left|{\mathrm{\α}}_i{g}_i\right|}^2{\mathrm{\σ}}_i^2+{\mathrm{\σ}}_D^2}---\left(2\right)$

Wherein,

|| || 2 norms of representation vector.

About i relaying, P _iRepresent its transmitted power, then to incoherent and dry type amplification mode mutually, relaying amplification factor α _iBe respectively

${\mathrm{\α}}_i^{\mathrm{non}-\mathrm{coh}}=\sqrt{\frac{P_i}{{\left|h_i\right|}^2{P}_s+{\mathrm{\σ}}_i^2}}---\left(3\right)$

${{\mathrm{\α}}_i}^{\mathrm{coh}}=\sqrt{\frac{P_i}{{\left|h_i\right|}^2{P}_s+{{\mathrm{\σ}}_i}^2}}\frac{g_i^{*}}{\left|g_i\right|}\frac{h_i^{*}}{\left|h_i\right|}---\left(4\right)$

(3) are obtained the same result with (4) difference substitutions (2), namely

$\mathrm{SNR}=\underset{i\∈R}{\mathrm{\Σ}}\frac{\frac{P_s{\left|h_i\right|}^2}{{\mathrm{\σ}}_i^2}\·\frac{P_i{\left|g_i\right|}^2}{{\mathrm{\σ}}_D^2}}{1+\frac{P_s{\left|h_i\right|}^2}{{\mathrm{\σ}}_i^2}+\frac{P_i{\left|g_i\right|}^2}{{\mathrm{\σ}}_D^2}}---\left(5\right)$

Suppose that the source node transmitted power is fixed as P _s, all relayings are subjected to the constraint with power, each relaying is subjected to simultaneously to retrain with the independent power of bound, represent relaying with Q and power constraint,

Represent the lower limit power constraint of i relaying,

Represent the Upper Bound Power constraint of i relaying.Satisfy simultaneously and the condition of power constraint and independent power constraint under, ask relaying optimal power allocation strategy, so that the maximization of the SNR shown in the formula (5).The abbreviation formula is as follows, note

x _i=P _i, $a_i=\frac{(P_s{\left|h_i\right|}^2+{\mathrm{\σ}}_i^2){\mathrm{\σ}}_D^2}{P_s{\left|h_i{g}_i\right|}^2},$ $b_i=\frac{{\mathrm{\σ}}_i^2}{P_s{\left|h_i\right|}^2},$ $\∀i\∈R---\left(6\right)$

Be defined as follows function:

$f(x_1,...,x_K)=\underset{i\∈R}{\mathrm{\Σ}}\frac{x_i}{a_i+b_i{x}_i}---\left(7\right)$

Then, above-mentioned power optimization problem representation is:

$\left\{\begin{array}{c}\{{\hat{x}}_i,i\∈R\}=\arg \underset{x_i,i\∈R}{\max }f(x_1,...,x_K)\\ \begin{array}{ccc}s.t.& x_i\≥Q_{b_i}& (\∀i\∈R)\end{array}\\ \begin{array}{cc}{x}_i\≤Q_{t_i}& (\∀i\∈R)\end{array}\\ \underset{i\∈R}{\mathrm{\Σ}}{x}_i\≤Q.\end{array}\right.---\left(8\right)$

(8) (9) are out of shape to get in arrangement:

$\left\{\begin{array}{c}\{{\hat{t}}_i,i\∈R\}=\arg \max f(t_1,...t_K)\\ \begin{array}{ccc}s.t.& t_i\≥0& (\∀i\∈R)\end{array}\\ t_i\≤Q_{t_i}-Q_{b_i}(\∀i\∈R)\\ \underset{i\∈R}{\mathrm{\Σ}}{t}_i\≤Q-\underset{i\∈R}{\mathrm{\Σ}}{Q}_{b_i}\end{array}\right.---\left(9\right)$

Wherein $f(t_1,...t_K)=\underset{i\&Element;R}{\mathrm{\&Sigma;}}\frac{t_i+Q_{b_i}}{a_i+b_i(t_i+Q_{b_i})},$ $t_i=x_i-Q_{b_i}(\&ForAll;i\&Element;R),$ $Q_{b_i}<Q_{t_i}(\&ForAll;i\&Element;R).$

As long as the optimal solution of (9) According to

Just can get the optimal solution of (8)

Suppose that destination node knows the signal transmitting power of source node, all the variance of noise component(s)s and system overall situation CSI.First find the solution formula (9) in destination node, then find the solution the corresponding power amplification factor by (4), last, destination node feeds back to corresponding relaying with the power amplification factor undistortedly.

Its concrete steps and being analyzed as follows:

Because of target function f (t ₁..., t _K) about independent variable

On [0 ,+∞], be monotonic increase, therefore need minute following three kinds of situations to ask the optimal solution of (9):

If 1..

Constraint (9) is inoperative so, again because f (t ₁..., t _K) about each independent variable t _iMonotonic increase, therefore the optimal solution of (9) is

If 2.. $Q-\underset{i\&Element;R}{\mathrm{\&Sigma;}}{Q}_{b_i}\&le;\min \{Q_{t_i}-Q_{b_i}\},$ Then constraints (9) is inoperative.

If 3.. $\min \{Q_{t_i}-Q_{b_i}\}>Q-\underset{i\&Element;R}{\mathrm{\&Sigma;}}{Q}_{b_i}<\underset{i\&Element;R}{\mathrm{\&Sigma;}}(Q_{t_i}-Q_{b_i})$ Then institute's Constrained concurs.

Beneficial effect: meaning of the present invention is via node is carried out having added in the process of power division the factor of processing of circuit power, has proposed the optimal power allocation method under a kind of combined power constraint.Wherein, the combined power constraint refers to have simultaneously the constraint of relaying independent power and relaying and the power constraint of bound constraint.So that model meets the actual conditions of many relay wireless collaborative network more.

Description of drawings

Fig. 1 wireless cooperative network model of the present invention.

Fig. 2 radiating circuit module of the present invention.

Fig. 3 receiving circuit module of the present invention.

Embodiment

Further describe thought of the present invention below in conjunction with accompanying drawing.

Fig. 1 is wireless cooperative network model of the present invention.

As shown in Figure 1, system is by a transmitting node S, and a receiving node D and k via node consist of.Each via node only has an antenna to be used for transmitting and receiving signal.With transmitting node S to i via node R _iBetween channel f _iExpression is with i via node R _iTo the channel g between the receiving node D _iExpression.

Fig. 2 is radiating circuit module of the present invention, and Fig. 3 is receiving circuit module of the present invention.

In order to introduce the processing of circuit power of via node, this paper will take into account Optimized model for the processing of circuit module that transmits and receives signal.According to document [Cui Shuguang, Goldsmith A J, Bahai A.Energy constrained modulation optimization[J] .IEEE Transactions on wireless communications, 2005,4 (5): 2349-2360] as can be known, each via node transmits and receives circuit module as shown in Figures 2 and 3.

(1) situation 2 times

Because target function f (t ₁... t _k) about each t _i[0 ,+all be monotonically increasing on ∞), therefore can be equality constraint with inequality constraints formula (9) abbreviation, be expressed as:

$\left\{\begin{array}{c}\{{\hat{t}}_i,i\&Element;R\}=\underset{t_{i}i\&Element;R}{\arg \max f(t_1,...t_K)}\\ \begin{array}{ccc}s.t.& t_i\&GreaterEqual;0& (\&ForAll;i\&Element;R)\end{array}\\ \underset{i\&Element;R}{\mathrm{\&Sigma;}}{t}_i=Q-\underset{i\&Element;R}{\mathrm{\&Sigma;}}{Q}_{b_i}\end{array}\right.---\left(10\right)$

The optimal solution of formula (10) can be expressed as:

${\hat{t}}_i={(\frac{1}{b_i}(\sqrt{\frac{a_i}{\mathrm{\&lambda;}}}-a_i)-Q_{b_i})}^{+},\&ForAll;i\&Element;R---\left(11\right)$

Wherein, λ is constant, and this constant can make all

Satisfy constraints (5.10b), (x) ⁺=max{0, x} it should be noted that (11) only are the expression formula of (10) optimal solution, next will provide the concrete algorithm of formula (11).

Define two set as follows:

$R_1=\left\{i\right|{\hat{t}}_i>0,i\&Element;R\},R_2=\{i|{\hat{t}}_i=0,i\&Element;R\}---\left(12\right)$

Then all the indexed set R of relaying can be expressed as R=R ₁∪ R ₂With R shown in the formula (12) ₁∪ R ₂The optimum segmentation that is called the corresponding R of formula (10).

Bottom provides required three theorems using of formula (10) optimal solution algorithm.Theorem 1 provides the R optimum segmentation Candidate Set shown in the formula (12); When theorem 2 provides the optimum segmentation of known R, the analytic expression of the optimal solution of formula (10); Theorem 3 has provided from theorem 1 and has provided the method for seeking optimum segmentation all elements of Candidate Set.

Theorem 1 is to a in (6) ₁, a ₂... a _kOrdering, suppose:

a _σ(1)≤a _σ(2)≤…a _σ(K)

Then gather total K the element of R optimum segmentation Candidate Set, that is:

$R_1^k=\{\mathrm{\&sigma;}\left(1\right),...\mathrm{\&sigma;}\left(k\right)\},$ $R_2^k=R\backslash R_1^k=\{\mathrm{\&sigma;}(k+1),...\mathrm{\&sigma;}\left(K\right)\},$ k=1,2,…K (13)

Wherein, extreme situation is Symbol The expression empty set, ∪ represents union of sets.

The optimum segmentation R of R shown in if theorem 2 formulas (12) are known ₁∪ R ₂, then in formula (10) optimal solution For

${\hat{t}}_i=\frac{\mathrm{\&epsiv;}\sqrt{a_i}-a_i}{b_i}-Q_{b_i},$ $\&ForAll;i\&Element;R_1---\left(14\right)$

Wherein,

$\mathrm{\&epsiv;}=\frac{Q-\underset{i\&Element;R}{\mathrm{\&Sigma;}}{Q}_{b_i}+\underset{i\&Element;R_1}{\mathrm{\&Sigma;}}{Q}_{b_i}+\underset{i\&Element;R_1}{\mathrm{\&Sigma;}}\frac{a_i}{b_i}}{\underset{i\&Element;R_1}{\mathrm{\&Sigma;}}\frac{\sqrt{a_i}}{b_i}}---\left(15\right)$

The maximum of target function is in the formula (10)

$f_{\max }=\underset{i\&Element;R_1}{\mathrm{\&Sigma;}}\frac{1}{b_1}-\frac{1}{\mathrm{\&epsiv;}}\frac{\sqrt{a_i}}{b_i}---\left(16\right)$

Theorem 5.3 definition $f\left(k\right)=f_{\max }^k=\underset{i\&Element;R_1}{\mathrm{\&Sigma;}}\frac{1}{b_1}-\frac{1}{\mathrm{\&epsiv;}}\frac{\sqrt{a_i}}{b_i},$ k=1,2,…K

Wherein,

Shown in (13), then must have:

f(K)>f(K-1)>…f(1) (17)

(2) situation 3 times

Part in the optimum results in the formula (9)

Reached upper limit binding occurrence, remaining does not reach, again f (t ₁... t _K) be monotonically increasing about each independent variable, therefore inequality constraints formula (9) can be simplified to equality constraint:

$\left\{\begin{array}{c}\{{\hat{t}}_i,i\&Element;R\}=\underset{t_i,i\&Element;R}{\arg \max }f(t_1,...t_K)\\ \begin{array}{ccc}s.t.& t_i\&GreaterEqual;0& (\&ForAll;i\&Element;R)\end{array}\\ t_i\&le;Q_i-Q_{b_i}(\&ForAll;i\&Element;R)\\ \underset{i\&Element;R}{\mathrm{\&Sigma;}}{t}_i=Q-\underset{i\&Element;R}{\mathrm{\&Sigma;}}{Q}_{b_i}.\end{array}\right.---\left(18\right)$

The optimal solution of formula (18) is

${\hat{t}}_i={(\frac{1}{b_i}(\sqrt{\frac{a_i}{\mathrm{\&lambda;}}}-a_i)-Q_{b_i})}_0^{Q_i-Q_{b_i}},$ $\&ForAll;i\&Element;R---\left(19\right)$

Wherein λ can make whole

Satisfy the constant of constraint formula (18), it should be noted that formula (19) only is the expression formula of the optimal solution of formula (18), next will provide the algorithm of calculating formula (18).

According to formula (19), the relaying indexed set is decomposed into two mutual exclusion set

$W_1=\left\{i\right|{\hat{t}}_i<Q_i-Q_{b_i},i\&Element;R\},$ $W_2=\left\{i\right|{\hat{i}}_i=Q_i-Q_{b_i},i\&Element;R\}---\left(20\right)$

R=W with (20) definition ₁∪ W ₂The optimum segmentation that is called (18) corresponding R.

Next provide two theorems, can draw the algorithm of formula (18) optimal solution by these two theorems.

Theorem 4 is defined as follows sequence

${\mathrm{\&eta;}}_i=\frac{a_i}{(a_i+b_i{Q}_i)},$ $\&ForAll;i\&Element;R$

Suppose

η _σ(1)≤η _σ(2)…≤η _σ(K)

Then have K element in the Candidate Set of R optimum segmentation shown in (20), that is:

$W_1^k=\{\mathrm{\&sigma;}\left(1\right),...\mathrm{\&sigma;}\left(k\right)\},$ $W_2^k=R\backslash W_1^k=\{\mathrm{\&sigma;}(k+1),...\mathrm{\&sigma;}\left(K\right)\},$ k=1,2,…K (21)

Central extreme case is

Theorem 5 orders

With

It is represented such as (21),

Optimal solution for corresponding (18).Be defined as follows discrete function:

$g\left(k\right)=f({\hat{t}}_l^k,...,{\hat{t}}_K^k),$ k=1,2,…K

Then have

g(K)≥g(K-1)≥…g(1) (22)

Claims (1)

1. the optimal power allocation method of many relayings under the frequency flatness fading channel, it is characterized in that: for the parallel direct scale-up version junction network of the double bounce in the frequency-flat channel decline situation, and in the situation of the processing of circuit power of consideration node self, provide the optimal power allocation method under a kind of combined power constraint; Wherein, the combined power constraint refers to have simultaneously the constraint of relaying independent power and relaying and the power constraint of bound constraint, and the method may further comprise the steps:

A. data by source node in the transmission course of destination node, in the first time slot, source node transmits to whole via nodes, destination node is in closed condition;

B. follow-up In the individual time slot, source node is in closed condition, and each time slot only has a via node to pass data to destination node, remaining

Individual via node all is in closed condition;

Individual via node is successively to the destination node the transmission of data; Process

Behind the individual time slot, all via node is all finished once with destination node and is communicated by letter, and each relaying is only communicated by letter once; The

During individual relaying work, it to the received signal first

Power is amplified, and the signal after will amplifying again transmits toward destination node, wherein,

Be the number of time slot,

Expression receives signal,

C. pass through Behind the time slot, source node can be regarded a single input multiple output system as to destination node;

D. about Individual relaying supposes that the source node transmitted power is fixed as

, each relaying is subjected to simultaneously to retrain with the independent power of bound, uses

The expression relaying and power constraint,

Represent

The lower limit power constraint of relaying,

Represent

The constraint of the Upper Bound Power of relaying, satisfy simultaneously and the condition of power constraint and independent power constraint under, ask relaying optimal power allocation strategy, then the abbreviation formula is as follows, note

,

,

Wherein

The ordinal number of expression via node, Expression the

The transmitted power of individual via node;

Be the channel coefficients of source node to via node; The expression signal variance; The variance of expression noise;

Represent

Individual via node is to the channel coefficients of destination node;

The indexed set that represents whole relayings, namely

Be defined as follows function:

Then, above-mentioned power optimization problem representation is:

Expression

Estimated value; Arrangement is out of shape

Wherein

Expression

Estimated value,

,

,

E. suppose that destination node knows the signal transmitting power of source node, all the variance of noise component(s)s; First find the solution following formula in destination node, then find the solution the corresponding power amplification factor, last, destination node feeds back to corresponding relaying with the power amplification factor undistortedly;

F. because of target function

About independent variable

(

)

On be monotonic increase, therefore need minute following three kinds of situations ask optimal solution:

If 1..

, retrain so inoperative, again because

About each independent variable Monotonic increase, so optimal solution is

If 2..

, then constraints is inoperative;

If 3..

Then institute's Constrained concurs.

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